How to remove a protrusion from a surface?
This is what everyone's talking about with Booleans: The Boolean modifier.



using the "difference" operation, wherever the sword object intersects the cube object, its volume is excluded.

Here's what it looks like without the head:


The surface of the volume you subtract from the sword can be as complex as you need; you could use the head object, for example. Be careful though because the boolean modifier is computationally expensive and prone to error. Stick to simple, unsbdivided manifold meshes with only one part to them for the best chance of success.

Edit: Here's the .blend file :